Moon's position to 10 arcsec

I have implemented the algorithm for finding the mean geocentric
longitude and latitude of the Moon which forms chapter 30 of Jean Meeus' book
Astronomical Formulas for Calculators. I have written a simple QBASIC program based on the algorithm, and modified the program to produce
daily Moon positions for the whole of a 'Saros' cycle of about 18.6 years ending around J2000.

I compared values from the Meeus algorithm with a series generated using
Manfred Ding's
Ephtool Lite ephemeris program, together with his DLL
implementing the full ELP-2000/82 analytical lunar theory.

The error in latitude when compared with ELP-2000/82 follows an expected pattern, but the
error in longitude shows a systematic difference of 35 arcseconds (posibly part of a long
period cycle) even after correction for nutation. The RMS error in longitude is 5 arcsec.

Below is the longitude error after applying a simple correction for nutation in longitude:

The error in latitude has an RMS of 3 arcsec, and the error curve looks symmetrical about
zero
error - there is no systematic error apparent.

Any ideas regarding the systematic error welcome. Otherwise, I shall produce a 'fudge
factor' to keep the algorithm accurate for fifty years either side of J2000.0